A GaN-based semiconductor device typified by a blue LED is manufactured by layering an n layer, light emitting layer and p layer on a single crystal substrate by epitaxial growth, and as the substrate, a sapphire single crystal substrate and SiC single crystal substrate are generally used. However, for example, since lattice mismatch exists between a sapphire crystal and a GaN-based semiconductor crystal, dislocations occur due to the lattice mismatch (for example, see Non-patent Document 1). The dislocation density reaches 1×109/cm2. By the dislocations, internal quantum efficiency decreases inside the LED, and as a result, luminous efficiency of the LED decreases.
Further, since the refractive index of the GaN-based semiconductor layer is larger than that of the sapphire substrate, light generated in the semiconductor light emitting layer is not emitted at angles of the critical angle or more from an interface with the sapphire substrate, the light becomes waveguide mode and is attenuated, and there is a problem that external quantum efficiency decreases as a result. Meanwhile, in the case of using the SiC substrate such that the refractive index is extremely larger than that of an air layer as the single crystal substrate, light is not emitted at angles of the critical angle or more from an interface between the SiC substrate and the air layer. Therefore, as in the case of using the sapphire substrate, emitted light generated in the semiconductor light emitting layer becomes waveguide mode and is attenuated, and there is a problem that external quantum efficiency decreases.
Therefore, such a technique is proposed that a substrate is provided with concavities and convexities that do not develop defects in the semiconductor to change the light waveguide direction of light in the semiconductor layer and that external quantum efficiency is thereby increased (for example, see Patent Document 1).
Further, another technique for a sapphire substrate is proposed in which the size of the concavo-convex structure provided on the substrate is nano-size and a pattern of the concavo-convex structure is of a random arraignment (for example, see patent Document 2). In addition, it is reported that when the pattern size provided on the substrate is nano-size, luminous efficiency of an LED is increased as compared with a pattern substrate of micro-size (for example, see Non-patent Document 2). Moreover, a GaN-based semiconductor device is proposed in which a concavo-convex structure is provided on the upper surface of a p-type semiconductor layer to reduce contact resistance with a transparent conductive film (for example, see Patent Document 3).